Optimal pricing and base stock determination in a multiclass M/G/1 make-to-stock queue

In this study, the problem of profit maximization of a single-server multiclass queuing system is analyzed. Customer demands follow independent Poisson processes and service times have general distribution. The demand is assumed to decrease linearly as the price increases. For each arrival, an order is placed to the server and a single queue is formed under FIFO discipline. If the on-hand inventory is not enough to satisfy the demand, then unsatisfied orders are backordered. Different backorder costs and price levels are considered for each customer class. Holding cost is incurred for the on-hand items in the inventory.Firstly, model formulation of the average profit function is developed. It is analyzed under an M/M/1 make-to-stock system. Then, optimal base stock level of an M/G/1 make-to-stock system is formulated. The dynamics of profit functions of M/M/1 make-to-stock systems are analyzed by trying different base stock levels under a single price. A convex approximation of the sum of holding and backorder costs over arrival rates is proposed to obtain optimal pricing and base stock level. Base stock levels are determined by using approximate optimal arrival rates. An algorithm is proposed to improve the results of the approximation. Approximations are tested under various parameters and service time distributions.